## Section: Scientific Foundations

### Ontology alignments

When different representations are used, it is necessary to identify their correspondences. This task is called ontology matching and its result is an alignment. It can be described as follows: given two ontologies, each describing a set of discrete entities (which can be classes, properties, rules, predicates, etc.), find the relationships, e.g., equivalence or subsumption, if any, that hold between these entities.

An alignment between two ontologies *o* and ${o}^{\prime}$ is a set of
correspondences $\langle e,{e}^{\prime},r\rangle $ in which

$e$ and ${e}^{\prime}$ are the entities between which a relation is asserted by the correspondence, e.g., formulas, terms, classes, individuals;

*r*is the relation asserted to hold between*e*and ${e}^{\prime}$. This relation can be any relation applying to these entities, e.g., equivalence, subsumption.

Given the semantics of the two ontologies provided by their consequence relation, we define an interpretation of two aligned ontologies as a pair interpretations $\langle m,{m}^{\prime}\rangle $, one for each ontology. Such a pair of interpretations is a model of the aligned ontologies $o$ and ${o}^{\prime}$ if and only if each respective interpretation is a model of the ontology and they satisfy all correspondences of the alignment.

This definition is extended to networks of ontologies: a set of ontologies and associated alignments. A model of such an ontology network is a tuple of local models such that each alignment is valid for the models involved in the tuple. In such a system, alignments play the role of model filters which will select the local models which are compatible with all alignments.

So, given an ontology network, it is possible to interpret it. However, given a set of ontologies, it is necessary to find the alignments between them and the semantics does not tell which ones they are. Ontology matching aims at finding these alignments. A variety of methods is used for this task. They perform pairwise comparisons of entities from each of the ontologies and select the most similar pairs. Most matching algorithms provide correspondences between named entities, more rarely between compound terms. The relationships are generally equivalence between these entities. Some systems are able to provide subsumption relations as well as other relations in the support language (like incompatibility or instanciation). Confidence measures are usually given a value between 0 and 1 and are used for expressing preferences between two correspondences.